Using a 32 bit grayscale TIFF in the displace modifier
You can convert a .tiff file to a .exr file using blender.



First switch to the Node editor





Next in the bottom panel you will see a box with 3 buttons in it click on the right one. Also enable 'use nodes' and 'backdrop'.



Next add an input. 'Shift + A' Input > Image. Navigate to your image you would like to convert.



Next add an output. 'Shift + A' Output > Composite.




You now should have something like this.



Thats all the nodes you need. Next you will need to change the render settings.

You will need to change the render size to the size of your image. You can get this by in you file browser RMB on the file properties > details. Change the output type to EXR (not multi-layer) and make sure that its set to 'float full' not 'float (half)' full is 32-bit half is 16-bit. Make you sure you know where you are saving the image. 



Next hit render and wait for it to render. Should be pretty fast though.





If that does not work you can you use irfanview to export the tiff into a different file format. Here is how. First open irfanview.



Then open your file you want to convert.



Choose 'File' > 'Save As'





Chose where you want to save it and the format.